Conflict in formulas P = IR^2 and P=delta v/r

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The discussion revolves around the apparent conflict between the equations P = IR^2 and P = ΔV/R, with participants clarifying that the assumptions about constant variables are crucial. When current is held constant, increasing resistance leads to increased power, while with constant voltage, increasing resistance reduces current and thus power. The confusion stems from the need to specify which factors are constant in each scenario. The conversation emphasizes the importance of understanding the context in which these formulas apply, particularly in series versus parallel circuits. Ultimately, the key takeaway is that the relationship between resistance and power is dependent on the conditions of the circuit.
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P = IR^2 and P=delta v/r

Did the first equation is Joules heating law, which shows that power increases with resistance. The 2nd equation which is given as an answer in my problem set states that a decrease in resistance increases power. The inconsistency is really bothering me. Help please
 

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Perseverence said:
P = IR^2 and P=delta v/r

Did the first equation is Joules heating law, which shows that power increases with resistance. The 2nd equation which is given as an answer in my problem set states that a decrease in resistance increases power. The inconsistency is really bothering me. Help please
It depends what is being held constant.
In I2R, increasing resistance will increase power assuming current is constant.
What assumption does the other equation make? Can both these assumptions be true at once?
 
the information I am trying to glean is the effect of increasing resistance on power when all other factors are constant.
 
Perseverence said:
the information I am trying to glean is the effect of increasing resistance on power when all other factors are constant.
So try to answer the questions I posed.
 
Perseverence said:
the information I am trying to glean is the effect of increasing resistance on power when all other factors are constant.
Can you get the relation P=I2R from P=ΔV2/R?
What does ΔV stand for here?
 
cnh1995 said:
Can you get the relation P=I2R from P=ΔV2/R?
What does ΔV stand for here?
Yes, I was just about to point out that P=ΔV/R makes no sense. It should of course be V2/R.
 
Please refer to the attached image for clarification.
 
Yes, it is Delta V squared. My apologies. V stands for VOLTAGE
 
haruspex said:
Yes, I was just about to point out that P=ΔV/R makes no sense. It should of course be V2/R.
Actually, I was referring to the attached image. Yes, the OP made a typo, but my question was to see if the OP can relate the two formulae.:smile:
Perseverence said:
V stands for VOLTAGE
Right, but voltage "across" what? Can you derive one formula from the other?
 
  • #10
Both of the equations assume that all other factors are constant. One is essentially Ohm's law. Given that all other factors are constant what would be the effect of increasing resistance on power
 
  • #11
Perseverence said:
Both of the equations assume that all other factors are constant. One is essentially Ohm's law. Given that all other factors are constant what would be the effect of increasing resistance on power
What is the effect of increasing resistance on the current through the resistance?
 
  • #12
cnh1995 said:
What is the effect of increasing resistance on the current through the resistance?
... if voltage is constant.
 
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  • #13
Ah, okay. I see it you can derive one equation from the other. They do seem at first to be in conflict. But it does still seem to be somewhat contradictory that in one instance resistance is directly proportional power and in the other it is inversely proportional.

It's still twists my brain a bit. I guess the rule is that when all other factors are constant decreasing resistance increases power.
 
  • #14
Thanks ! This was my first pos to this forum and you guys were great :)
 
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  • #15
Perseverence said:
It's still twists my brain a bit. I guess the rule is that when all other factors are constant decreasing resistance increases power.
That is true if the voltage across the resistance remains constant i.e. in case of a circuit containing parallel resistances connected across a voltage source.

If you have a series circuit containing two resistors r and R in series with a constant voltage source, and you are changing R keeping all the other parameters constant, you can't make the above statement about the power dissipated in R. Look up 'maximum power transfer' theorem.
 
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  • #16
cnh1995 said:
That is true if the voltage across the resistance remains constant i.e. in case of a circuit containing parallel resistances connected across a voltage source.

If you have a series circuit containing two resistors r and R in series with a constant voltage source, and you are changing R keeping all the other parameters constant, you can't make the above statement about the power dissipated in R. Look up 'maximum power transfer' theorem.
cnh1995 said:
That is true if the voltage across the resistance remains constant i.e. in case of a circuit containing parallel resistances connected across a voltage source.

If you have a series circuit containing two resistors r and R in series with a constant voltage source, and you are changing R keeping all the other parameters constant, you can't make the above statement about the power dissipated in R. Look up 'maximum power transfer' theorem.
Makes sense. Thank you
 
  • #17
Perseverence said:
Makes sense. Thank you
No probs!
And welcome to PF!:smile:
 
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  • #18
Perseverence said:
I guess the rule is that when all other factors are constant decreasing resistance increases power.
No, this is why I asked the questions I asked. You cannot hold all else constant. With voltage constant, increasing resistance reduces current and power; with current constant (by some means) increasing resistance increases voltage and power.
 
  • #19
haruspex said:
No, this is why I asked the questions I asked. You cannot hold all else constant. With voltage constant, increasing resistance reduces current and power; with current constant (by some means) increasing resistance increases voltage and power.
Yes, I understand what you were saying now.
 
  • #20
Perseverence said:
Yes, I understand what you were saying now.
Thank you. Your statement helps me understand this concept a lot more
 

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